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Handbook of Conformal Mapping with Computer-Aided Visualization



ISBN 9780849389368
Published December 16, 1994 by CRC Press
368 Pages

 
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Book Description

This book is a guide on conformal mappings, their applications in physics and technology, and their computer-aided visualization. Conformal mapping (CM) is a classical part of complex analysis having numerous applications to mathematical physics. This modern handbook on CM includes recent results such as the classification of all triangles and quadrangles that can be mapped by elementary functions, mappings realized by elliptic integrals and Jacobian elliptic functions, and mappings of doubly connected domains. This handbook considers a wide array of applications, among which are the construction of a Green function for various boundary-value problems, streaming around airfoils, the impact of a cylinder on the surface of a liquid, and filtration under a dam.
With more than 160 domains included in the catalog of mapping, Handbook of Conformal Mapping with Computer-Aided Visualization is more complete and useful than any previous volume covering this important topic. The authors have developed an interactive ready-to-use software program for constructing conformal mappings and visualizing plane harmonic vector fields. The book includes a floppy disk for IBM-compatible computers that contains the CONFORM program.

Table of Contents

Mathematics: The Theory of Conformal Mappings
Complex Plane, Domains and Curves on It
The Analytic Functions of a Complex Variable
Conjugate Harmonic Functions
The Geometric Meaning of the Derivative; Isogonal and Local Conformal Mappings
Univalent Analytic Functions. Conformal Mappings of Domains
General Principles of the Theory of Conformal Mappings
Conformal Mappings Realized by the Basic Elementary Functions
Isothermic Coordinates. Differential Operators in the Isothermic Coordinates
Mappings of Lunes
The Construction of Conformal Mappings with the Help of the Boundary Correspondence Principle
The Construction of Conformal Mappings of Curvilinear Strips with the Help of an Analytic Continuation of a Function from the Real Axis
The Mapping of Polygonal Domains. Schwarz-Christoffel Integral
Mappings of Rectangular Domains. Elliptic Integrals and Elliptic Functions
Conformal Mapping of Doubly Connected Domains
Physics: Applications of Conformal Mappings
Insight into Plane Harmonic Vector Field
Plane Harmonic Vector Fields in Physics
Complex Potential
Boundary-Value Problems for Harmonic Functions
The Construction of a Green Function of the Dirichlet Problem
The Green Function of the Neumann Problem
The Green Function of a Mixed Boundary-Value Problem
Point Source and Sink in the Dirichlet Problem
Point Source and Sink in the Neumann Problem
Plane Robin Problem
The Flow in a Curvilinear Angular Domain. Streaming Around an Infinite Curve
The Flow in a Curvilinear Strip
The Flow in a Curvilinear Strip with N Branches
The Flow Running onto an Infinite Curve and Branching on It
Irrotational Streaming Around a Finite Contour
Mixed Boundary-Value Problem in a Curvilinear Angular Domain. The Simplest Problem of the Filtration Theory
Distribution of the Electric Current in a Plate in the Presence of Two Non-Point Electrodes at Its Boundary
The General Problem on the Streaming Around a Finite Contour
The Problem on the Impact of a Solid Cylinder upon the Surface of a Non-Compressible Liquid
The Flow with Branching in a Curvilinear Strip with N Branches
Practice: Catalog of Conformal Mappings
Finite Domains
Exteriors of Finite Contours
Curvilinear Angular Domains
Curvilinear Strips
Curvilinear Strips with N Branches
Appendix: Program CONFORM

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Author(s)

Biography

Ivanov\, Valentin I.; Trubetskov\, Michael K.